Yes, the bonus spells must go on a qualifying class's spell list
It's not included in the specific description of each bloodline feat, but those feats are preceded by a preamble about the nature of bloodline feats in general, which describes that:
Each of the base feats in this category (the ones with the word "bloodline" in their names) grants a character the bloodline of a particular kind of magical creature, plus a specific set of extra arcane spells known. If more than one of her classes allows her to cast arcane spells without preparation, the character must decide to which list of spells known the spells granted by the base bloodline feat are added when the it [sic] is chosen.
It could be phrased more precisely than it is, since the wording isn't proof against someone intent on an unnatural RAW reading - but the clear intent is that the bonus spells should be added to a spontaneous arcane casting class's list, not another kind of casting class you may have, since you are only expected to have a choice about which class list you add it to if you are a member of more than one such class.
You should also be aware that the text of rules on D&D Tools and similar resources is often incomplete and in some cases rephrased or altered in such a way that it actually changes meaning, so it's best to track down the primary sources if you can.